First-Price auction symmetric equlibria with a general distribution

In this paper I obtain the mixed strategy symmetric equilibria of the first-price auction for any distribution. The equilibrium is unique. The solution turns out to be a combination of absolutely continuous distributions case and the discrete distributions case.

First-price auction symmetric equilibria with a general distribution

In this paper I obtain the mixed strategy symmetric equilibria of the first-price auction for any distribution. The equilibrium is unique. The solution turns out to be a combination of absolutely continuous distributions case and the discrete distributions case.

Synergies and price trends in sequential auctions

In this paper we consider sequential auctions where an individual’s value for a bundle of objects is either greater than the sum of the values for the objects separately (positive synergy) or less than the sum (negative synergy). We show that the existence of positive synergies implies declining expected prices. When synergies are negative, expected prices are increasing. There are several corollaries. First, the seller is indi¤erent between selling the objects simultaneously as a bundle or sequentially when synergies are positive. Second, when synergies are negative, the expected revenue generated by the simultaneous auction can be larger or smaller than the expected revenue generated by the sequential auction. In addition, in the presence of positive synergies, an option to buy the additional object at the price of the …rst object is never exercised in the symmetric equilibrium and the seller’s revenue is unchanged. Under negative synergies, in contrast, if there is an equilibrium where the option is never exercised, then equilibrium prices may either increase or decrease and, therefore, the net e¤ect on the seller’s revenue of the introduction of an option is ambiguous. Finally, we examine two special cases with asymmetric players. In the …rst case, players have distinct synergies. In this example, even if one player has positive synergies and the other has negative synergies, it is still possible for expected prices to decline. In the second case, one player wants two objects and the remaining players want one object each. For this example, we show that expected prices may not necessarily decrease as predicted by Branco (1997). The reason is that players with singleunit demand will generally bid less than their true valuations in the …rst period. Therefore, there are two opposing forces; the reduction in the bid of the player with multiple-demand in the last auction and less aggressive bidding in the …rst auction by the players with single-unit demand.

The effect of options on coordination

This paper studies how constraints on the timing of actions affect equilibrium in intertemporal coordination problems. The model exhibits a unique symmetric equilibrium in cut-o¤ strategies. The risk-dominant action of the underlying one-shot game is selected when the option to delay effort is commensurate with the option to wait longer for others' actions. The possibility of waiting longer for the actions of others enhances coordination, but the option of delaying one s actions can induce severe coordination failures: if agents are very patient, they might get arbitrarily low expected payoffs even in cases where coordination would yield arbitrarily large returns.

Contágio no modelo de Allen e Gale com infraestrutura bancária endógena

Neste trabalho investigamos a formação de network considerando agentes cautelosos. O modelo consiste em duas regiões com (n/2) bancos em cada, onde a interligação entre eles ocorre através e depósitos interbancários. Cada banco está sujeito a corrida bancária, ou devido a um choque negativo de agentes impacientes, ou devido a contaminação da corrida de um banco pertencente a infraestrutura bancária. Os bancos podem tentar eliminar a possibilidade de contágio ao fazer um número alto de inter-ligações. Para isso, é necessário uma coordenação entre todos os bancos. Se um banco não se prevenir de um contágio, ele impõe a todos os outros a possibilidade de contágio no pior cenário. Há duas regiões bem definidas de equilíbrio de nash simétrico com network estável, uma na qual todos os bancos se previnem do cenário de contágio no pior cenário e a outra na qual nenhum banco se previne. Devido ao problema de coordenação, o equilíbrio com contágio no pior cenário pode ocorrer mesmo sendo pareto dominado pelo equilíbrio sem contágio. Sob certas condições, o equilíbrio com contágio ocorre com um network pareto eficiente. Neste caso o network eficiente é diferente do network mais resiliente ao contágio.